diff --git a/colossalai/zero/low_level/low_level_optim.py b/colossalai/zero/low_level/low_level_optim.py
index e3c301640..24ebae1c7 100644
--- a/colossalai/zero/low_level/low_level_optim.py
+++ b/colossalai/zero/low_level/low_level_optim.py
@@ -18,6 +18,7 @@ from colossalai.amp.naive_amp.mixed_precision_mixin import (
     FP16MixedPrecisionMixin,
     MixedPrecisionMixin,
 )
+from colossalai.checkpoint_io.utils import calculate_tensor_size
 from colossalai.interface import OptimizerWrapper
 from colossalai.logging import get_dist_logger
 from colossalai.quantization.fp8 import all_gather_fp8, all_reduce_fp8, reduce_scatter_fp8
@@ -865,19 +866,17 @@ class LowLevelZeroOptimizer(OptimizerWrapper):
 
             for k, v in states.items():
                 if isinstance(v, torch.Tensor) and k != "step":
-                    if pinned_state_dicts and k not in pinned_state_dicts[param_idx]:
-                        pinned_state_dicts[param_idx][k] = torch.empty_like(
-                            working_param, pin_memory=True, device="cpu"
-                        )
                     state_tensor = torch.empty(v.numel() * get_nd_world_size(pg), device=device, dtype=v.dtype)
                     all_gather_into_flat_tensor_nd(state_tensor, v.to(device).flatten(), pg)
                     state_tensor = state_tensor[: working_param.numel()].reshape_as(working_param)
+                    if pinned_state_dicts and k not in pinned_state_dicts[param_idx]:
+                        pinned_state_dicts[param_idx][k] = torch.empty_like(state_tensor, pin_memory=True, device="cpu")
                     if pinned_state_dicts:
                         pinned_state_dicts[param_idx][k].copy_(state_tensor)
                         current_block[k] = pinned_state_dicts[param_idx][k]
                     else:
                         current_block[k] = state_tensor.cpu()
-                    current_block_size += state_tensor.numel()
+                    current_block_size += calculate_tensor_size(state_tensor)
 
             if ret_block_size + current_block_size > max_shard_size and len(ret_block) > 0:
                 yield ret_block, ret_block_size